The mean velocity of slightly buoyant and heavy particles in turbulent flow in a pipe

1958 ◽  
Vol 4 (1) ◽  
pp. 87-96 ◽  
Author(s):  
A. M. Binnie ◽  
O. M. Phillips
Keyword(s):  
Turbulent Flow ◽  
Relative Density ◽  
Terminal Velocity ◽  
Neutral Density ◽  
Mean Velocity ◽  
Heavy Particles ◽  
Horizontal Pipe ◽  
The Mean ◽  
The Times

A large number of small spheres of the same size were injected successively into a horizontal pipe conveying water at constant mean velocity, and their times of transit were measured. The mean velocity of the spheres that were either somewhat heavier or lighter than water was less than that of those of neutral density; for those having a terminal velocity in water within ± 1% of the mean velocity of the water in the pipe, the discrepancy was only about 0.1%. The dispersion of the times of transit of the spheres was almost independent of their density. A theory is developed to show how the mean velocity of the spheres depends upon their relative density and size.

The vertical diffusivity and mean velocity of particles in a horizontal water pipe

1963 ◽  
Vol 15 (1) ◽  
pp. 35-48 ◽  
Author(s):  
B. J. S. Barnard ◽  
A. M. Binnie
Keyword(s):  
Relative Density ◽  
Cross Section ◽  
Terminal Velocity ◽  
Galvanized Steel ◽  
Water Pipe ◽  
Mean Velocity ◽  
Vertical Diffusivity ◽  
The Mean ◽  
The Times

Small spheres of the same size but of relative density varying from 0·92 to 1·25 were injected in turn into a horizontal water pipe, in which the flow was turbulent and the mean velocity was constant. A cross-section near the outlet was illuminated; the positions of the spheres as they crossed it were measured by photography, and the relation was established between the terminal velocity of the of the spheres in water and the vertical diffusivity. The velocity of the spheres along the pipe was found to be somewhat different in the galvanized steel and Perspex lengths of which the pipe was composed. The dispersion of the times of transit of the spheres increased slightly with their densisty. For purposes of comparison the theoretical velocity along the pipe was also calculated from the photographic measurements.

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

Turbulent Statistics of Nearly Isotropic Turbulence Generated by Four Rotating Grids and the Mean Falling Velocity of Particle Through Turbulence

2007 ◽  
Author(s):  
Tatsuo Ushijima ◽  
Osami Kitoh
Keyword(s):  
Isotropic Turbulence ◽  
Terminal Velocity ◽  
Mean Velocity ◽  
Velocity Autocorrelation ◽  
Air Turbulence ◽  
Turbulent Statistics ◽  
Experimental Apparatus ◽  
Particle Property ◽  
The Mean ◽  
Lda Measurement

Box air turbulence is experimentally generated in a rectangular box by using four counter-rotating grids installed inside. Turbulence statistics are obtained from one-point measurement of LDA. Nearly isotropic turbulence with zero-mean velocity is realised in the midst of four rotating grids. The dissipation rate is estimated from the Taylor time microscale of velocity autocorrelation obtained from LDA measurement, since Taylor’s frozen turbulence hypothesis is not applicable. From this estimation, the Reynolds number based on the Taylor length microscale becomes about 200 at maximum in the present experimental apparatus. The mean falling velocity of small particle in turbulent flow is measured in the box turbulence. It is found that the mean falling velocity of the inertia particle could be smaller or larger than the terminal velocity, depending on the particle property, if the ratios of particle response time to turbulence time scale are the same.

Measurements with a pulsed-wire and a hot-wire anemometer in the highly turbulent wake of a normal flat plate

1976 ◽  
Vol 77 (3) ◽  
pp. 473-497 ◽  
Author(s):  
L. J. S. Bradbury
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Flow Direction ◽  
Operating Conditions ◽  
Turbulent Intensity ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Better Than

This paper describes an investigation into the response of both the pulsed-wire anemometer and the hot-wire anemometer in a highly turbulent flow. The first part of the paper is concerned with a theoretical study of some aspects of the response of these instruments in a highly turbulent flow. It is shown that, under normal operating conditions, the pulsed-wire anemometer should give mean velocity and longitudinal turbulent intensity estimates to an accuracy of better than 10% without any restriction on turbulence level. However, to attain this accuracy in measurements of turbulent intensities normal to the mean flow direction, there is a lower limit on the turbulent intensity of about 50%. An analysis is then carried out of the behaviour of the hot-wire anemometer in a highly turbulent flow. It is found that the large errors that are known to develop are very sensitive to the precise structure of the turbulence, so that even qualitative use of hot-wire data in such flows is not feasible. Some brief comments on the possibility of improving the accuracy of the hot-wire anemometer are then given.The second half of the paper describes some comparative measurements in the highly turbulent flow immediately downstream of a normal flat plate. It is shown that, although it is not possible to interpret the hot-wire results on their own, it is possible to calculate the hot-wire response with a surprising degree of accuracy using the results from the pulsed-wire anemometer. This provides a rather indirect but none the less welcome check on the accuracy of the pulsed-wire results, which, in this very highly turbulent flow, have a certain interest in their own right.

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

scholarly journals HYSTERESIS AND VORTICES DYNAMICS IN A TURBULENT FLOW

2009 ◽  
Vol 19 (08) ◽  
pp. 2695-2703 ◽  
Author(s):  
JAVIER BURGUETE ◽  
ALBERTO DE LA TORRE
Keyword(s):  
Turbulent Flow ◽  
Additive Noise ◽  
Potential Model ◽  
Time Dependent ◽  
Small Range ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
Bistable Regime ◽  
The Mean

Recent results about the slow dynamics present in a fully developed turbulent flow are reported. In a previous paper [de la Torre & Burguete, 2007] we showed that the mean velocity field in a turbulent flow bifurcates subcritically breaking some symmetries of the problem and becomes time-dependent because of equatorial vortices moving with a precession movement. This subcriticality produces a bistable regime, whose main characteristics were successfully reproduced using a three-well potential model with additive noise. In this paper we present the characterization of the hysteresis region, not previously observed, in this bifurcation. This hysteresis appears only for an extremely small range of parameters.

STEADY STATE HEAT TRANSFER TO FULLY DEVELOPED TURBULENT FLOW IN A CURVED CHANNEL

1957 ◽  
Vol 35 (4) ◽  
pp. 410-434
Author(s):  
A. W. Marris
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Mean Flow ◽  
Curved Channel ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
Angular Velocities ◽  
The Mean

A vorticity transfer analogy theory of turbulent heat transfer is developed first for the case of fully developed turbulent flow under zero transverse pressure and temperature gradients such as that in the annulus between concentric cylinders rotating with different angular velocities or in a "free vortex". The mean flow is assumed to be two-dimensional. The theory, which requires that the turbulence be statistically isotropic, yields a temperature distribution in agreement with experiment except in narrow regions immediately adjacent to the boundaries. An argument is given to show that the boundary layer thickness should be of the order of the reciprocal of the square root of the mean velocity, these boundaries are introduced, and Nusselt moduli are defined and their dependence on Reynolds and Prandtl numbers is investigated.The temperature distributions for the case of non-zero transverse temperature and pressure gradients, i.e. for the case of flow in a curved channel in which the fluid does not flow back into itself, are then obtained and the applicability of the simpler equations for zero transverse gradients to this case is investigated.

scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

scholarly journals Raindrop fall velocity in turbulent flow: an observational study

2021 ◽  
Vol 18 ◽  
pp. 33-39
Author(s):  
Merhala Thurai ◽  
Viswanathan Bringi ◽  
Patrick Gatlin ◽  
Mathew Wingo
Keyword(s):  
Turbulent Flow ◽  
Gold Standard ◽  
Sonic Anemometer ◽  
Terminal Velocity ◽  
Laboratory Measurements ◽  
Air Velocity ◽  
Fall Velocity ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Rain Events

Abstract. Laboratory measurements of drop fall speeds by Gunn–Kinzer under still air conditions with pressure corrections of Beard are accepted as the “gold standard”. We present measured fall speeds of 2 and 3 mm raindrops falling in turbulent flow with 2D-video disdrometer (2DVD) and simultaneous measurements of wind velocity fluctuations using a 3D-sonic anemometer. The findings based on six rain events are, (i) the mean fall speed decreases (from the Gunn–Kinzer terminal velocity) with increasing turbulent intensity, and (ii) the standard deviation increases with increase in the rms of the air velocity fluctuations. These findings are compared with other observations reported in the literature.

The Present State of the Turbulence Problem

1933 ◽  
Vol 1 (1) ◽  
pp. 19-28
Author(s):  
Walter Tollmien
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Theory ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Fully Developed Turbulence ◽  
Developed Turbulence ◽  
The Mean ◽  
Real Goal

Abstract In this survey the author first describes certain types of turbulent flow, following which he deals successively with the production of turbulent motion; the instability of the laminar motion; fully developed turbulence; momentum interchange and mixing lengths; and relations between the shearing stress at the wall and the mean velocity distributions. Finally he takes up the calculation of skin friction for simple cases of fully developed turbulence, especially for that of the flat plate. Although the methods outlined have often led to practically useful results, it is the author’s belief that they should be considered only as advances toward the real goal of the turbulence theory. The derivation of turbulence phenomena from the hydrodynamical equations will, in his opinion, be possible only by the application of statistical methods.

Sign in / Sign up

Export Citation Format

Share Document